💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Watch this step-by-step video, matched to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Take $\mathbf{q}$ on the line segment from $\mathbf{b}$ to $\mathbf{c}$ and consider the linethrough $\mathbf{q}$ and $\mathbf{a},$ which may be written as $\mathbf{p}=(1-x) \mathbf{q}+x \mathbf{a}$ $x \cdot \operatorname{det}[\tilde{\mathbf{a}} \quad \tilde{\mathbf{b}} \quad \tilde{\mathbf{c}}] .$ From this and earlier work, conclude that the parameter $x$ is the first barycentric coordinate of $\mathbf{p} .$ However, by construction, the parameter $x$ also determines the relative distance between $\mathbf{p}$ and $\mathbf{q}$ along the segment from q to a. (When $x=1, \mathbf{p}=\mathbf{a} . )$ When this fact is applied to Example $5,$ it shows that the colors at vertex $\mathbf{a}$ and the point $\mathbf{q}$ are smoothly interpolated as $\mathbf{p}$ moves along the line between $\mathbf{a}$ and $\mathbf{q}$

See answer

Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 2

Affine Independence

Vectors

Johns Hopkins University

Campbell University

Oregon State University

Baylor University

Lectures

02:56

In mathematics, a vector (…

06:36

03:20

Show that the points $P=(a…

0:00

(a) Let $ P $ be a point n…

09:30

(a) Let $P$ be a point not…

05:12

Assign coordinates to each…

01:43

A point $P(x, y)$ is on th…

02:00

Midpoint of a line segment…

08:10

Suppose that the coordinat…

02:46

Consider the line segment …

04:31

Show that a vertex $c$ in …

03:31

Find(a) the distance b…

no For this question, let's p equals one minus x Q plus x A. We're Q is on the line. Segments underlines segments. Be so See now determinants. If you write this as determinants off pizza, either b t the seats you the will be equal to determinant off. Just put it suitor on the Q and then on the A you're gonna have one minus specs. Cute. See the lost eggs It soother then beat you the on dhe see sealed. You can't write these. You can write this because on this is like the forced Coolum rights from one of the properties of determinants. You can write this as did some minutes off one minus excuse either. Then be on dhe, see lost determinants off. Ex es su the B and see. You can confirm these that you can always writes. You can always split the first columns into this song off the detail off the determinants. Similarly, you can take out the multiplication, so this is one minus x more supply by determinants off cubes. You the beats you with sits you either loss. You can pull us on eggs because it's on the first column ex Mort supplied by determinants off, it's you beats you see, Silda, No things. Q is on the line segments okay, probably should just do this way. So from here we have that Cuba is on the line Segments B and C. That's implies that's Q. Is in Lena combination off vectors Be on C on. This would also mean dots Que Tsuda is a linear combination off that does be sued on C. So because Q Iselin a commission off be executed as an inner commission of beauty down sit Sudha, that implies that the metrics memories it is weak. This implies on metrics. Cute. See the Additionally a comedy because it's just columns. Cute you, the beats you the seeped through the He's single up because one of the colossus the linear combination of the other columns this were implied that the determinants off cutely would beat you. That seats you. He called to zero. So from say, for example, equation star. So this is a zero tsunamis that's determinants off from star. We have done determinants off pizza. The beats you sits you the record to ex multiplied by determinants off eight Suder beats Judah and then see

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Show that the points $P=(a, b)$ and $Q=(b, a)$ are symmetric with respect to…

(a) Let $ P $ be a point not on the line $ L $ that passes through the point…

(a) Let $P$ be a point not on the line $L$ that passes through thepoints…

Assign coordinates to each vertex and write a coordinate proof.Given: $\…

A point $P(x, y)$ is on the curve $y=x^{2}+1$(a) Express the distance fr…

Midpoint of a line segment Use vectors to show that the midpoint of the line…

Suppose that the coordinates of points $P, Q,$ and $M$ are$$\begin{array…

Consider the line segment joining the points $P\left(x_{0}, y_{0}, z_{0}\rig…

Show that a vertex $c$ in the connected simple graph $G$ is a cut vertex if …

Find(a) the distance between P and Q and (b) the coordinates of the …

03:51

Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}…

07:45

In Exercises $7-10$ , let $H$ be the hyperplane through the listed points. (…

05:20

Let$$\mathbf{v}_{1}=\left[\begin{array}{l}{1} \\ {0} \\ {3} \\ {0}\end{a…

03:23

Solve and check each of the equations.$x^{2}-9 x=10$

01:08

The sample covariance matrix is a generalization of a formula for the varian…

09:24

Classify the quadratic forms in Exercises $9-18 .$ Then make a change of var…

05:25

Repeat Exercise 1 where $m$ is the minimum value of $f$ on $S$ instead of th…

01:40

Exercises 23 and 24 show how to classify a quadratic form $Q(\mathbf{x})=\ma…

03:04

Solve and check each of the equations.$x^{2}-7 x+10=0$

03:55

Find an SVD of each matrix [Hint: In Exercise 11, one choice for $U$ is $\le…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.